Q26 of 153 Page 13

Find the number of solutions of z2 + |z|2 = 0.

Given:


⇒ z2+|z|2=0


Let us assume z=x+iy


⇒


⇒ x2+(iy)2+2(x)(iy)+x2+y2=0


⇒ 2x2+y2+i2y2+i2xy=0


We know that i2=-1


⇒ 2x2+y2-y2+i2xy=0


⇒ 2x2+i2xy=0


Equating Real and Imaginary parts on both sides we get,


⇒ 2x2=0 and 2xy=0


⇒ x=0 and yR


∴ z=0+iy where yR. i.e, Infinite solutions.


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